#include "blaswrap.h"
#include "f2c.h"

/* Subroutine */ int cppsvx_(char *fact, char *uplo, integer *n, integer *
	nrhs, complex *ap, complex *afp, char *equed, real *s, complex *b, 
	integer *ldb, complex *x, integer *ldx, real *rcond, real *ferr, real 
	*berr, complex *work, real *rwork, integer *info)
{
/*  -- LAPACK driver routine (version 3.0) --   
       Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,   
       Courant Institute, Argonne National Lab, and Rice University   
       June 30, 1999   


    Purpose   
    =======   

    CPPSVX uses the Cholesky factorization A = U**H*U or A = L*L**H to   
    compute the solution to a complex system of linear equations   
       A * X = B,   
    where A is an N-by-N Hermitian positive definite matrix stored in   
    packed format and X and B are N-by-NRHS matrices.   

    Error bounds on the solution and a condition estimate are also   
    provided.   

    Description   
    ===========   

    The following steps are performed:   

    1. If FACT = 'E', real scaling factors are computed to equilibrate   
       the system:   
          diag(S) * A * diag(S) * inv(diag(S)) * X = diag(S) * B   
       Whether or not the system will be equilibrated depends on the   
       scaling of the matrix A, but if equilibration is used, A is   
       overwritten by diag(S)*A*diag(S) and B by diag(S)*B.   

    2. If FACT = 'N' or 'E', the Cholesky decomposition is used to   
       factor the matrix A (after equilibration if FACT = 'E') as   
          A = U'* U ,  if UPLO = 'U', or   
          A = L * L',  if UPLO = 'L',   
       where U is an upper triangular matrix, L is a lower triangular   
       matrix, and ' indicates conjugate transpose.   

    3. If the leading i-by-i principal minor is not positive definite,   
       then the routine returns with INFO = i. Otherwise, the factored   
       form of A is used to estimate the condition number of the matrix   
       A.  If the reciprocal of the condition number is less than machine   
       precision, INFO = N+1 is returned as a warning, but the routine   
       still goes on to solve for X and compute error bounds as   
       described below.   

    4. The system of equations is solved for X using the factored form   
       of A.   

    5. Iterative refinement is applied to improve the computed solution   
       matrix and calculate error bounds and backward error estimates   
       for it.   

    6. If equilibration was used, the matrix X is premultiplied by   
       diag(S) so that it solves the original system before   
       equilibration.   

    Arguments   
    =========   

    FACT    (input) CHARACTER*1   
            Specifies whether or not the factored form of the matrix A is   
            supplied on entry, and if not, whether the matrix A should be   
            equilibrated before it is factored.   
            = 'F':  On entry, AFP contains the factored form of A.   
                    If EQUED = 'Y', the matrix A has been equilibrated   
                    with scaling factors given by S.  AP and AFP will not   
                    be modified.   
            = 'N':  The matrix A will be copied to AFP and factored.   
            = 'E':  The matrix A will be equilibrated if necessary, then   
                    copied to AFP and factored.   

    UPLO    (input) CHARACTER*1   
            = 'U':  Upper triangle of A is stored;   
            = 'L':  Lower triangle of A is stored.   

    N       (input) INTEGER   
            The number of linear equations, i.e., the order of the   
            matrix A.  N >= 0.   

    NRHS    (input) INTEGER   
            The number of right hand sides, i.e., the number of columns   
            of the matrices B and X.  NRHS >= 0.   

    AP      (input/output) COMPLEX array, dimension (N*(N+1)/2)   
            On entry, the upper or lower triangle of the Hermitian matrix   
            A, packed columnwise in a linear array, except if FACT = 'F'   
            and EQUED = 'Y', then A must contain the equilibrated matrix   
            diag(S)*A*diag(S).  The j-th column of A is stored in the   
            array AP as follows:   
            if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;   
            if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.   
            See below for further details.  A is not modified if   
            FACT = 'F' or 'N', or if FACT = 'E' and EQUED = 'N' on exit.   

            On exit, if FACT = 'E' and EQUED = 'Y', A is overwritten by   
            diag(S)*A*diag(S).   

    AFP     (input or output) COMPLEX array, dimension (N*(N+1)/2)   
            If FACT = 'F', then AFP is an input argument and on entry   
            contains the triangular factor U or L from the Cholesky   
            factorization A = U**H*U or A = L*L**H, in the same storage   
            format as A.  If EQUED .ne. 'N', then AFP is the factored   
            form of the equilibrated matrix A.   

            If FACT = 'N', then AFP is an output argument and on exit   
            returns the triangular factor U or L from the Cholesky   
            factorization A = U**H*U or A = L*L**H of the original   
            matrix A.   

            If FACT = 'E', then AFP is an output argument and on exit   
            returns the triangular factor U or L from the Cholesky   
            factorization A = U**H*U or A = L*L**H of the equilibrated   
            matrix A (see the description of AP for the form of the   
            equilibrated matrix).   

    EQUED   (input or output) CHARACTER*1   
            Specifies the form of equilibration that was done.   
            = 'N':  No equilibration (always true if FACT = 'N').   
            = 'Y':  Equilibration was done, i.e., A has been replaced by   
                    diag(S) * A * diag(S).   
            EQUED is an input argument if FACT = 'F'; otherwise, it is an   
            output argument.   

    S       (input or output) REAL array, dimension (N)   
            The scale factors for A; not accessed if EQUED = 'N'.  S is   
            an input argument if FACT = 'F'; otherwise, S is an output   
            argument.  If FACT = 'F' and EQUED = 'Y', each element of S   
            must be positive.   

    B       (input/output) COMPLEX array, dimension (LDB,NRHS)   
            On entry, the N-by-NRHS right hand side matrix B.   
            On exit, if EQUED = 'N', B is not modified; if EQUED = 'Y',   
            B is overwritten by diag(S) * B.   

    LDB     (input) INTEGER   
            The leading dimension of the array B.  LDB >= max(1,N).   

    X       (output) COMPLEX array, dimension (LDX,NRHS)   
            If INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X to   
            the original system of equations.  Note that if EQUED = 'Y',   
            A and B are modified on exit, and the solution to the   
            equilibrated system is inv(diag(S))*X.   

    LDX     (input) INTEGER   
            The leading dimension of the array X.  LDX >= max(1,N).   

    RCOND   (output) REAL   
            The estimate of the reciprocal condition number of the matrix   
            A after equilibration (if done).  If RCOND is less than the   
            machine precision (in particular, if RCOND = 0), the matrix   
            is singular to working precision.  This condition is   
            indicated by a return code of INFO > 0.   

    FERR    (output) REAL array, dimension (NRHS)   
            The estimated forward error bound for each solution vector   
            X(j) (the j-th column of the solution matrix X).   
            If XTRUE is the true solution corresponding to X(j), FERR(j)   
            is an estimated upper bound for the magnitude of the largest   
            element in (X(j) - XTRUE) divided by the magnitude of the   
            largest element in X(j).  The estimate is as reliable as   
            the estimate for RCOND, and is almost always a slight   
            overestimate of the true error.   

    BERR    (output) REAL array, dimension (NRHS)   
            The componentwise relative backward error of each solution   
            vector X(j) (i.e., the smallest relative change in   
            any element of A or B that makes X(j) an exact solution).   

    WORK    (workspace) COMPLEX array, dimension (2*N)   

    RWORK   (workspace) REAL array, dimension (N)   

    INFO    (output) INTEGER   
            = 0:  successful exit   
            < 0:  if INFO = -i, the i-th argument had an illegal value   
            > 0:  if INFO = i, and i is   
                  <= N:  the leading minor of order i of A is   
                         not positive definite, so the factorization   
                         could not be completed, and the solution has not   
                         been computed. RCOND = 0 is returned.   
                  = N+1: U is nonsingular, but RCOND is less than machine   
                         precision, meaning that the matrix is singular   
                         to working precision.  Nevertheless, the   
                         solution and error bounds are computed because   
                         there are a number of situations where the   
                         computed solution can be more accurate than the   
                         value of RCOND would suggest.   

    Further Details   
    ===============   

    The packed storage scheme is illustrated by the following example   
    when N = 4, UPLO = 'U':   

    Two-dimensional storage of the Hermitian matrix A:   

       a11 a12 a13 a14   
           a22 a23 a24   
               a33 a34     (aij = conjg(aji))   
                   a44   

    Packed storage of the upper triangle of A:   

    AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]   

    =====================================================================   


       Parameter adjustments */
    /* Table of constant values */
    static integer c__1 = 1;
    
    /* System generated locals */
    integer b_dim1, b_offset, x_dim1, x_offset, i__1, i__2, i__3, i__4, i__5;
    real r__1, r__2;
    complex q__1;
    /* Local variables */
    static real amax, smin, smax;
    static integer i__, j;
    extern logical lsame_(char *, char *);
    static real scond, anorm;
    extern /* Subroutine */ int ccopy_(integer *, complex *, integer *, 
	    complex *, integer *);
    static logical equil, rcequ;
    extern doublereal clanhp_(char *, char *, integer *, complex *, real *), slamch_(char *);
    extern /* Subroutine */ int claqhp_(char *, integer *, complex *, real *, 
	    real *, real *, char *);
    static logical nofact;
    extern /* Subroutine */ int clacpy_(char *, integer *, integer *, complex 
	    *, integer *, complex *, integer *), xerbla_(char *, 
	    integer *);
    static real bignum;
    extern /* Subroutine */ int cppcon_(char *, integer *, complex *, real *, 
	    real *, complex *, real *, integer *);
    static integer infequ;
    extern /* Subroutine */ int cppequ_(char *, integer *, complex *, real *, 
	    real *, real *, integer *), cpprfs_(char *, integer *, 
	    integer *, complex *, complex *, complex *, integer *, complex *, 
	    integer *, real *, real *, complex *, real *, integer *), 
	    cpptrf_(char *, integer *, complex *, integer *);
    static real smlnum;
    extern /* Subroutine */ int cpptrs_(char *, integer *, integer *, complex 
	    *, complex *, integer *, integer *);
#define b_subscr(a_1,a_2) (a_2)*b_dim1 + a_1
#define b_ref(a_1,a_2) b[b_subscr(a_1,a_2)]
#define x_subscr(a_1,a_2) (a_2)*x_dim1 + a_1
#define x_ref(a_1,a_2) x[x_subscr(a_1,a_2)]


    --ap;
    --afp;
    --s;
    b_dim1 = *ldb;
    b_offset = 1 + b_dim1 * 1;
    b -= b_offset;
    x_dim1 = *ldx;
    x_offset = 1 + x_dim1 * 1;
    x -= x_offset;
    --ferr;
    --berr;
    --work;
    --rwork;

    /* Function Body */
    *info = 0;
    nofact = lsame_(fact, "N");
    equil = lsame_(fact, "E");
    if (nofact || equil) {
	*(unsigned char *)equed = 'N';
	rcequ = FALSE_;
    } else {
	rcequ = lsame_(equed, "Y");
	smlnum = slamch_("Safe minimum");
	bignum = 1.f / smlnum;
    }

/*     Test the input parameters. */

    if (! nofact && ! equil && ! lsame_(fact, "F")) {
	*info = -1;
    } else if (! lsame_(uplo, "U") && ! lsame_(uplo, 
	    "L")) {
	*info = -2;
    } else if (*n < 0) {
	*info = -3;
    } else if (*nrhs < 0) {
	*info = -4;
    } else if (lsame_(fact, "F") && ! (rcequ || lsame_(
	    equed, "N"))) {
	*info = -7;
    } else {
	if (rcequ) {
	    smin = bignum;
	    smax = 0.f;
	    i__1 = *n;
	    for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
		r__1 = smin, r__2 = s[j];
		smin = dmin(r__1,r__2);
/* Computing MAX */
		r__1 = smax, r__2 = s[j];
		smax = dmax(r__1,r__2);
/* L10: */
	    }
	    if (smin <= 0.f) {
		*info = -8;
	    } else if (*n > 0) {
		scond = dmax(smin,smlnum) / dmin(smax,bignum);
	    } else {
		scond = 1.f;
	    }
	}
	if (*info == 0) {
	    if (*ldb < max(1,*n)) {
		*info = -10;
	    } else if (*ldx < max(1,*n)) {
		*info = -12;
	    }
	}
    }

    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("CPPSVX", &i__1);
	return 0;
    }

    if (equil) {

/*        Compute row and column scalings to equilibrate the matrix A. */

	cppequ_(uplo, n, &ap[1], &s[1], &scond, &amax, &infequ);
	if (infequ == 0) {

/*           Equilibrate the matrix. */

	    claqhp_(uplo, n, &ap[1], &s[1], &scond, &amax, equed);
	    rcequ = lsame_(equed, "Y");
	}
    }

/*     Scale the right-hand side. */

    if (rcequ) {
	i__1 = *nrhs;
	for (j = 1; j <= i__1; ++j) {
	    i__2 = *n;
	    for (i__ = 1; i__ <= i__2; ++i__) {
		i__3 = b_subscr(i__, j);
		i__4 = i__;
		i__5 = b_subscr(i__, j);
		q__1.r = s[i__4] * b[i__5].r, q__1.i = s[i__4] * b[i__5].i;
		b[i__3].r = q__1.r, b[i__3].i = q__1.i;
/* L20: */
	    }
/* L30: */
	}
    }

    if (nofact || equil) {

/*        Compute the Cholesky factorization A = U'*U or A = L*L'. */

	i__1 = *n * (*n + 1) / 2;
	ccopy_(&i__1, &ap[1], &c__1, &afp[1], &c__1);
	cpptrf_(uplo, n, &afp[1], info);

/*        Return if INFO is non-zero. */

	if (*info != 0) {
	    if (*info > 0) {
		*rcond = 0.f;
	    }
	    return 0;
	}
    }

/*     Compute the norm of the matrix A. */

    anorm = clanhp_("I", uplo, n, &ap[1], &rwork[1]);

/*     Compute the reciprocal of the condition number of A. */

    cppcon_(uplo, n, &afp[1], &anorm, rcond, &work[1], &rwork[1], info);

/*     Set INFO = N+1 if the matrix is singular to working precision. */

    if (*rcond < slamch_("Epsilon")) {
	*info = *n + 1;
    }

/*     Compute the solution matrix X. */

    clacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
    cpptrs_(uplo, n, nrhs, &afp[1], &x[x_offset], ldx, info);

/*     Use iterative refinement to improve the computed solution and   
       compute error bounds and backward error estimates for it. */

    cpprfs_(uplo, n, nrhs, &ap[1], &afp[1], &b[b_offset], ldb, &x[x_offset], 
	    ldx, &ferr[1], &berr[1], &work[1], &rwork[1], info);

/*     Transform the solution matrix X to a solution of the original   
       system. */

    if (rcequ) {
	i__1 = *nrhs;
	for (j = 1; j <= i__1; ++j) {
	    i__2 = *n;
	    for (i__ = 1; i__ <= i__2; ++i__) {
		i__3 = x_subscr(i__, j);
		i__4 = i__;
		i__5 = x_subscr(i__, j);
		q__1.r = s[i__4] * x[i__5].r, q__1.i = s[i__4] * x[i__5].i;
		x[i__3].r = q__1.r, x[i__3].i = q__1.i;
/* L40: */
	    }
/* L50: */
	}
	i__1 = *nrhs;
	for (j = 1; j <= i__1; ++j) {
	    ferr[j] /= scond;
/* L60: */
	}
    }

    return 0;

/*     End of CPPSVX */

} /* cppsvx_ */

#undef x_ref
#undef x_subscr
#undef b_ref
#undef b_subscr


